\subsection{}
When there is no frozen fermi sea, the problem becomes a bit different.  There is no solution for weak attraction in the one-pair problem. (There is one, but approach zero at thermal dynamic limit.)  On the contrary, at many-body level, there is likely a solution for any attraction no matter how weak it is. (BCS solution?)  So when extending the one-pair to two-pair, one interesting problem is \emph{whether the threshold for attraction (the minimal attraction for existance of bound state) decreases}.  


\subsection{}
In some sense, the close-channel is in the dilute limit of cobosons. The coboson itself is much smaller than the inter-particle distance and still smaller even with the open-channel considered.  So can we simply use the correction from the dilute coboson $f_n$